Yes, sometimes converting diamonds is inevitable. The lowest gold cost of leveling Gold primarch is 14,5M, but to even hire one you need 18,5M. You can get 18,9M space in your storage only at player level 325. OP is talking under 300.
120 diamonds for raiding is equivalent to approx. 136k gold.
For free to play players, the 5x multiplier on beasts is a measely 30k gold. Even on a sapphire team with a 100% gold bonus, the payout is still only 60k. I’m sure it’s a lot easier in diamond and with elite, but you gotta realize the perspective lol
Without elite on my 100% gold bonus, I can only farm about 4.5M gold a day using my 30x-10x multipliers. Considering that the prim upgrades are upwards of 15M, it’s inevitable to spend diamonds and/or large sums of gold packs.
To answer OP’s question, it’s what ZooperJooper said. Make sure to use all your multipliers every day and save every diamond and every drop of gold you can get. Join an atlas active team with bonuses. Do well in atlas events. It’s a very long process, and to be honest, I don’t think you should worry about leveling your prims. Just play the game normally and the prim levels will come naturally.